Question

A small publishing company is planning to publish a new book. The production costs will include one-time fixed costs (such as editing) and variable costs (such as printing). There are two production methods it could use. With one method, the one-time fixed costs will total $ 60,346 , and the variable costs will be $ 10.50 per book. With the other method, the one-time fixed costs will total $ 18,682 , and the variable costs will be $ 21 per book. For how many books produced will the costs from the two methods be the same? books

Answer 1

Equation :

$10.50x \: + 60346 = 21x \: + 18682$

Move terms,

$10.5x + 60346 = 21x \\ \: \: \: \: \: \: \: \: \: \: \: \: - \: 18682 =41664$

Move terms again,

$41664 = 21x \\ \: \: \: \: \: \: \: \: \: \: \: \: \: - \: 10.5x = 10.5x$

Rewrite,

$41664 = 10.5x$

Divide both sides by 10.5x,

$3968 = x$

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Answer :

If 3,968 books are produced the costs form the two methods will be the same.

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I hope that helps you out!!

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~Zoey

Answer 2

Suppose x books are produced by both methods.
Total cost for method 1 = 60346 + 10.5x
Total cost for method 2 = 18682 + 21x

Cost of method 1 = Cost of method 2
60346 + 10.5x = 18682 + 21x
60346 - 18682 = 21x - 10.5x
41664 = 10.5x
x = 41664/10.5
x = 3968

For 3968 books produced the cost by both methods will be the same.